# A Unified Approach to Mitigate Voltage Jump Effects in Near Optimal Switching Surface Control of DC-DC Converters

## TL;DR

This paper models ESR-induced voltage jumps in DC-DC converters using Jump-Flow Switched systems, and proposes a non-jumping control approach with a practical analog implementation for improved stability and performance.

## Contribution

It introduces a novel modeling of ESR effects with Jump-Flow Switched systems and develops a non-jumping control method for near optimal switching surface control.

## Key findings

- The proposed controller achieves fast, robust responses in experiments.
- It effectively eliminates voltage jumps caused by ESR.
- The control method avoids chattering and hysteresis, simplifying implementation.

## Abstract

The Equivalent Series Resistance (ESR) of the output capacitor may cause output voltage Vo jumps, that are not modeled commonly for second order DC-DC converters, i.e., converters with two second order switched subsystems. These jump discontinuities in Vo lead to performance issues in Switching Surface (SS) controllers. In this paper, these ESR effects are modeled using switched systems with state jumps, called Jump-Flow Switched (JFS) systems. Furthermore, it is shown that approximating the capacitor voltage (Vc), with Vo, can cause undesired limit cycles, oscillations, chattering or instability issues. To resolve these issues, a non-jumping normal switched system is defined for JFS systems, that is equivalent to the internal continuous dynamics. Also, the challenges of designing SS controllers, for this equivalent switched system is studied, and the Constrained Near Optimal (CNO) SS is designed for the equivalent switched system of buck, boost, and buck-boost converters. To eliminate the required estimations, a general class of switching methods are defined, that also avoids chattering and eliminates the conventional hysteresis blocks. The proposed controller is implemented using analog op-amp circuits. Experimental results show fast and robust responses of the controller board with buck, boost, and buck-boost converters.

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Source: https://tomesphere.com/paper/1903.09966